By Pablo Bachelet

WASHINGTON, Oct 23 (Reuters) - Defying a White House veto threat, the U.S. Senate on Thursday approved a measure that eliminates funding to enforce a travel ban to communist Cuba.

The approval came in a voice vote after Senators voted 59-36 to overcome a procedural motion that would have effectively killed the initiative.

Supporters of the funding block said the long-standing U.S. travel ban had failed to oust Cuban President Fidel Castro and was unfair to Americans, who can travel to North Korea but not Cuba.

“For 40 years we’ve said ‘sanctions,’ and for 40 years it hasn’t worked,” said Sen. Mike Enzi, a Wyoming Republican, one of six bipartisan co-sponsors of the measure.

The Senate vote is significant because supporters of the travel ban had managed previously managed to prevent the funding measure from coming to a vote in the Senate. The House of Representative passed an identical amendment on Sept. 9, by a 227-188 vote.

“A very strong majority of the Senate supports the freedom of Americans to travel to Cuba and supports engagement as a best way to bring democratic reform to Cuba,” said Jody Frisch, a director of U.S. Engage, which worked to lift the ban.

Only a restricted group of U.S. citizens, which includes members of Congress, business leaders and journalists, can travel legally to Cuba, though tens of thousands more do so through Canada and Mexico.

President George W. Bush has taken a firm stance on the Cuba travel ban, announcing on Oct. 10 he had instructed officials to toughen enforcement.

Addressing a group of Cuban exiles from Miami, whose votes are crucial in the 2004 presidential elections, Bush said: “The Castro regime will not change by its own choice. But Cuba must change.”

The White House argues that travelers are herded into tourist enclaves, with minimal contact with locals, and their dollars used to prop up a dictatorship.

Travel ban opponents say the fact that both houses of Congress have the same language makes it harder to strip out the measure, an amendment included in a larger Transportation and Treasury appropriation bill, once it goes to conference committee.

The White House has vowed to veto the overall spending bill if it contains language on Cuba.

Sen. Byron Dorgan, a North Dakota Democrat and one of the amendment’s sponsors, said the administration should focus on catching terrorists, not travelers. He cited a Homeland Security Department memo which said it would use “intelligence and investigative resources” to identify travelers to Cuba.

“That’s Byzantine. It makes no sense,” Dorgan said during the debate on the Senate floor.

A determined group of lobbyists have been trying to get Congress to chip away at the travel ban. On Sunday, a group of travel executives met with Castro, who thanked them for their efforts to get the ban overturned.

Cuba expects as many as 1 million American visitors in the first year after the ban ends.